Abstract
It is of common use in modern Venn diagrams to mark a compartment with a cross to express its non-emptiness. Modern scholars seem to derive this convention from Charles S. Peirce, with the assumption that it was unknown to John Venn. This paper demonstrates that Venn actually introduced several methods to represent existentials but felt uneasy with them. The resistance to formalize existentials was not limited to diagrammatic systems, as George Boole and his followers also failed to provide a satisfactory symbolic representation for them. This difficulty points out issues that are inherent to the very nature of existentials. This paper assesses the various methods designed for the representation of existential statements with Venn diagrams. First, Venn’s own attempts are discussed and compared with other solutions proposed by his contemporaries and successors, notably Lewis Carroll and Peirce. Since disjunctives hold an important role in an effective representation of existentials, their representation is also discussed. Finally, recent methods for the diagrammatic representation of existing individuals, rather than mere existence, are surveyed.
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Acknowledgments
This paper draws upon research supported by Estonian Research Council PUT 267 “Diagrammatic mind: logical and communicative aspects of iconicity,” Principal investigator Prof. Ahti-Veikko Pietarinen. Parts of this paper were presented by the first author at the 13th International Congress of Logic, Methodology and Philosophy of Science (9–15 August 2007) in Beijing, China.
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Moktefi, A., Pietarinen, AV. On the Diagrammatic Representation of Existential Statements with Venn Diagrams. J of Log Lang and Inf 24, 361–374 (2015). https://doi.org/10.1007/s10849-015-9228-1
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DOI: https://doi.org/10.1007/s10849-015-9228-1